csat-suneung 2005 Q7

csat-suneung · South-Korea · csat__math-humanities 3 marks Sequences and series, recurrence and convergence Convergence proof and limit determination

For a sequence $\left\{ a _ { n } \right\}$ where the sum of the first $n$ terms $S _ { n } = 2 n + \frac { 1 } { 2 ^ { n } }$, what is the value of $\lim _ { n \rightarrow \infty } a _ { n }$? [3 points]
(1) 2
(2) 1
(3) $\frac { 1 } { 2 }$
(4) $\frac { 1 } { 4 }$
(5) 0

For a sequence $\left\{ a _ { n } \right\}$ where the sum of the first $n$ terms $S _ { n } = 2 n + \frac { 1 } { 2 ^ { n } }$, what is the value of $\lim _ { n \rightarrow \infty } a _ { n }$? [3 points]\\
(1) 2\\
(2) 1\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 1 } { 4 }$\\
(5) 0

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